Cavity Expansion in Rock Masses Obeying the “Hoek–Brown” Failure Criterion

Abstract

An unified approach is presented for the analysis of the expansion of both cylindrical and spherical cavities in an infinite elastic–perfectly plastic “Hoek–Brown” (H–B) material. The H–B failure criterion expressed in scaled form is adopted with a plastic flow rule characterized by a constant dilatancy angle $$\psi$$. Closed form expressions are given for the extent of the plastic region and the related stress. Solutions of the displacement field in the plastic region are provided based on both small-strain and large-strain theories. An original relationship between the cavity pressure and its expansion is derived. The developed closed-form solutions are validated employing the finite element method. For comparison purposes, an approximate solution is presented by neglecting the elastic strains in the plastic region which reveals that the assumption of no elastic strains does not influence the results for strong rocks in contrast with weak rocks. For practical purposes, design charts are provided allowing easy and accurate estimates of the limit pressure for cavity expansion in rock masses. The cavity expansion solution is finally validated against results obtained using the Finite Element modelling.